An alkaline storage battery having a negative electrode made from a hydrogen absorbing alloy represented by the formula Ln.sub.1-xMg.sub.xNi.sub.y-aM.sub.a (where Ln is at least one element selected from rare earth elements, M is at least one element selected from the group consisting of Al, V, Nb, Ta, Cr, Mo, Mn, Fe, Co, Ga, Zn, Sn, In, Cu, Si and P, 0.05.ltoreq.x<0.20, 2.8.ltoreq.y.ltoreq.3.9 and 0.10.ltoreq.a.ltoreq.0.50) and carbon as a conductive agent, a positive electrode of nickel hydroxide as an active material, and an alkaline electrolyte, and the alkaline storage battery contains not greater than 0.01 weight % of hydrogen or not greater than 0.13 weight % of water in the hydrogen absorbing alloy when the battery is activated and is discharged to 1.0 V at one hour rate (It).